2. A survey of 259 families was made to determine their vacation habits. The two way table below sorts the families by location and the vacations by the length of the vacation.
Rural Suburban Urban Total
1–7 days 80 39 37 156
8ormore days52 32 19 103
Total 132 71 56 259
What is the probability that a randomly selected family was suburban given that they spent 8 or more days on vacation? (1 point)
0.12
0.31
0.45
0.50
28.24
You draw one card from a shuffled standard deck of cards (cards are in four suits —red diamonds, red hearts, black clubs, and black spades— and are numbered 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A).
a) What is the probability of drawing a red card?
b) What is the probability of drawing a queen?
c) What is the probability of drawing a red queen?
d) What is the probability of drawing a queen given that you drew a face card (face cards are jacks, queens, and kings)?
32/259 = ?
I have already answered this second question in a previous post.
See Post under name of Helen.
Thanks
To find the probability that a randomly selected family was suburban given that they spent 8 or more days on vacation, we need to use conditional probability.
Conditional probability is the probability of an event happening given that another event has already occurred. In this case, the event is being suburban and the condition is spending 8 or more days on vacation.
To calculate conditional probability, we can use the formula:
P(A|B) = P(A ∩ B) / P(B)
Where P(A|B) is the probability of event A happening given that event B has already occurred, P(A ∩ B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.
From the given two-way table, we can see that there are 32 families who are suburban and spent 8 or more days on vacation. Therefore, P(A ∩ B) = 32.
The total number of families who spent 8 or more days on vacation is 103. Therefore, P(B) = 103.
Now, we can substitute these values into the conditional probability formula:
P(suburban|8ormore days) = P(suburban ∩ 8ormore days) / P(8ormore days)
= 32 / 103
Calculating this gives us approximately 0.3107. So, the probability that a randomly selected family was suburban given that they spent 8 or more days on vacation is approximately 0.31.
Therefore, the correct answer is 0.31.
Now, let's move on to the next set of questions about drawing cards from a shuffled standard deck.
a) What is the probability of drawing a red card?
To find the probability of drawing a red card, we need to determine the number of red cards and divide it by the total number of cards in the deck.
In a standard deck of cards, there are two red suits - diamonds and hearts. Each suit has 13 cards.
So, the total number of red cards in the deck is 2 (suits) x 13 (cards per suit) = 26.
The total number of cards in the deck is 4 (suits) x 13 (cards per suit) = 52.
Therefore, the probability of drawing a red card is 26/52 = 0.5 or 50%.
So, the correct answer is 0.50.
b) What is the probability of drawing a queen?
In a standard deck of cards, there are four queens - one in each suit.
So, the total number of queens in the deck is 4.
Again, the total number of cards in the deck is 52.
Therefore, the probability of drawing a queen is 4/52 = 1/13.
So, the correct answer is 1/13.
c) What is the probability of drawing a red queen?
From the previous calculations, we know that the probability of drawing a queen is 1/13.
Out of the four queens in the deck, two are red - the queen of diamonds and the queen of hearts.
Therefore, the probability of drawing a red queen is 2/52 = 1/26.
So, the correct answer is 1/26.
d) What is the probability of drawing a queen given that you drew a face card?
A face card refers to jacks, queens, and kings. Each suit has one of each face card, so there are a total of 3 face cards per suit.
In a standard deck of cards, there are a total of 12 face cards - 3 in each of the 4 suits.
So, the probability of drawing a face card is 12/52 = 3/13.
Out of the 12 face cards, 4 are queens.
Therefore, the probability of drawing a queen given that you drew a face card is 4/12 = 1/3.
So, the correct answer is 1/3.